where \(a_\mathrm {p}\)  is the activity of the lithium ions in the electrolyte. As such, \(\phi _\mathrm {e}\)  is closely related to the electrochemical potential of lithium ions in the electrolyte, \(\mu _{\mathrm {e}+}\) , via the equation \(\mu _{\mathrm {e}+} = F \phi _\mathrm {e}+ \text{constant}\) . This, as pointed out in [1]}, [2]}, [3]}, has led to numerous discrepancies in the literature. Another point to highlight is that the electrochemical transport theory underlying the concentrated electrolyte equations has been further developed in [4]}, [5]}, [6]}; in particular, streamlining thermodynamic foundations of the theory to account for temperature, pressure and stress effects, and clarifying the relationship between the chemical and electrical potentials. Finally, we want to highlight that, quite often, the gradient of the electrochemical potential is written in terms of \(f_{\pm }\) , the mean molal activity coefficient of the salt. From [7]} it can be seen that for a moderately concentrated electrolyte, the gradient of the chemical potential, \(\mu _\mathrm {e}\) , can be replaced by the expression
\(\nabla \mu _\mathrm {e}= RT \left( 1 + {\log f_\pm }{\log c_\mathrm {e}} \right) \nabla \log c_\mathrm {e}, \) 
